We have measured the central structural properties for a sample of S0-Sbc galaxies down to scales of similar to 10 pc using Hubble Space Telescope NICMOS images. Central star clusters are found in 58% of our sample. Their near-infrared luminosities scale with the host bulge luminosities, as reported in 2003 by Balcells and coworkers. In terms of photometric masses, the relation is M-PS = 10(7.75 +/- 0.15) (M-bul/10(10) M-circle dot)(0.76 +/- 0.13). Put together with recent data on bulges hosting supermassive black holes, we infer a nonlinear dependency of the 'central massive object' mass on the host bulge mass such that M-CMO/M-circle dot = 10(7.51 +/- 0.06)(M-bul/10(10)M(circle dot))(0.84 +/- 0.06). The linear relation presented by Ferrarese and co-workers may be biased at the low-mass end by the inclusion of the disk light from cluster lenticular galaxies. Bulge-disk decompositions reaching to the outer disk show that similar to 90% of our galaxies possess central light excesses that can be modeled with an inner exponential and/or an unresolved source. All the extended nuclear components, with sizes of a few hundred parsecs, have disky isophotes, which suggest that they may be inner disks, rings, or bars; their colors are redder than those of the underlying bulge, arguing against a recent origin for their stellar populations. Surface brightness profiles ( of the total galaxy light, and the bulge component on its own) rise inward to the resolution limit of the data, with a continuous distribution of logarithmic slopes from the low values typical of dwarf ellipticals (0.1 <= gamma <= 0.3) to the high values (gamma similar to 1) typical of intermediate-luminosity ellipticals; the nuclear slope bimodality reported by others is not present in our sample.